AES: wie wird die S-Box berechnet?

[Leo B. (luigi)]

Hallo zusammen,

für ein Vorlesung in der Uni möchte ich verstehen wie die AES im Detail 
funktioniert. Dazu habe ich einfach mal versucht selbigen in Matlab zu 
schreiben, was auch bisher recht erfolgreich war. Nur leider sitze ich 
heute schon fast den ganzen Nachmittag an der Berechnung der S-Boxen und 
scheitere daran.

Alle Dokumente und Unterlagen die ich bisher durchforstet habe 
beschrieben auf mehr oder weniger komplizierte weise das selbe, was auch 
bei Wikipedia in relativ einfacher Formulierung steht.
http://en.wikipedia.org/wiki/Rijndael_S-box

The matrix multiplication can be calculated by the following algorithm:

1. Store the multiplicative inverse of the input number in two 8-bit
   unsigned temporary variables: s and x.
2. Rotate the value s one bit to the left; if the value of s had a high
   bit (eighth bit from the right) of one, make the low bit of s one;
   otherwise the low bit of s is zero.
3. Exclusive OR the value of x with the value of s, storing the value in x
4. For three more iterations, repeat steps two and three; steps two and
   three are done a total of four times.
5. The value of x will now have the result of the multiplication.

After the matrix multiplication is done, exclusive or the value by the
decimal number 99 (the hexadecimal number 0x63, the binary number 1100011,
and the bit string 11000110 representing the number in LSb first notation).

Interessant ist nur, dass wenn ich das mache, ich auf ganz andere 
Ergebnisse komme.

Das Skript zum Ausprobieren (wie gesagt in Matlab-Code):

for i = uint8( 0:255 )
    s = i;
    x = i;
    
    for a=1:4
        s = bitor( bitshift( s, 1 ), bitshift( s, 1-8 ) );
        x = bitxor( x, s );
    end
    x = bitxor( x, hex2dec('63') );

    % zum Vergleich die sbox mit LookUp-Table
    sb = sbox( i );

    % ausgabe
    if x == sb
        s = '    equal';
    else
        s = 'not equal';
    end
    
    s = [ s sprintf( ': i = %2x(%s) ', i, dec2bin( i, 8 ) )...
            sprintf( '; x = %2x(%s) ', x, dec2bin( x, 8 ) )...
            sprintf( '; sbox = %2x(%s) ', sb, dec2bin( sb, 8 ) ) ];
    display( [s ''] ) ;
end

und was dabei raus kommt:

    equal: i = 0x00(00000000) ; x = 0x63(01100011) ; sbox = 0x63(01100011) 
    equal: i = 0x01(00000001) ; x = 0x7c(01111100) ; sbox = 0x7c(01111100) 
not equal: i = 0x02(00000010) ; x = 0x5d(01011101) ; sbox = 0x77(01110111) 
not equal: i = 0x03(00000011) ; x = 0x42(01000010) ; sbox = 0x7b(01111011) 
not equal: i = 0x04(00000100) ; x = 0x1f(00011111) ; sbox = 0xf2(11110010) 
not equal: i = 0x05(00000101) ; x = 0x00(00000000) ; sbox = 0x6b(01101011) 
not equal: i = 0x06(00000110) ; x = 0x21(00100001) ; sbox = 0x6f(01101111) 
not equal: i = 0x07(00000111) ; x = 0x3e(00111110) ; sbox = 0xc5(11000101) 
not equal: i = 0x08(00001000) ; x = 0x9b(10011011) ; sbox = 0x30(00110000) 
not equal: i = 0x09(00001001) ; x = 0x84(10000100) ; sbox = 0x01(00000001) 
not equal: i = 0x0a(00001010) ; x = 0xa5(10100101) ; sbox = 0x67(01100111) 
not equal: i = 0x0b(00001011) ; x = 0xba(10111010) ; sbox = 0x2b(00101011) 
not equal: i = 0x0c(00001100) ; x = 0xe7(11100111) ; sbox = 0xfe(11111110) 
not equal: i = 0x0d(00001101) ; x = 0xf8(11111000) ; sbox = 0xd7(11010111) 
not equal: i = 0x0e(00001110) ; x = 0xd9(11011001) ; sbox = 0xab(10101011) 
not equal: i = 0x0f(00001111) ; x = 0xc6(11000110) ; sbox = 0x76(01110110) 
not equal: i = 0x10(00010000) ; x = 0x92(10010010) ; sbox = 0xca(11001010) 
not equal: i = 0x11(00010001) ; x = 0x8d(10001101) ; sbox = 0x82(10000010) 
not equal: i = 0x12(00010010) ; x = 0xac(10101100) ; sbox = 0xc9(11001001) 
not equal: i = 0x13(00010011) ; x = 0xb3(10110011) ; sbox = 0x7d(01111101) 
not equal: i = 0x14(00010100) ; x = 0xee(11101110) ; sbox = 0xfa(11111010) 
not equal: i = 0x15(00010101) ; x = 0xf1(11110001) ; sbox = 0x59(01011001) 
not equal: i = 0x16(00010110) ; x = 0xd0(11010000) ; sbox = 0x47(01000111) 
not equal: i = 0x17(00010111) ; x = 0xcf(11001111) ; sbox = 0xf0(11110000) 
not equal: i = 0x18(00011000) ; x = 0x6a(01101010) ; sbox = 0xad(10101101) 
not equal: i = 0x19(00011001) ; x = 0x75(01110101) ; sbox = 0xd4(11010100) 
not equal: i = 0x1a(00011010) ; x = 0x54(01010100) ; sbox = 0xa2(10100010) 
not equal: i = 0x1b(00011011) ; x = 0x4b(01001011) ; sbox = 0xaf(10101111) 
not equal: i = 0x1c(00011100) ; x = 0x16(00010110) ; sbox = 0x9c(10011100) 
not equal: i = 0x1d(00011101) ; x = 0x09(00001001) ; sbox = 0xa4(10100100) 
not equal: i = 0x1e(00011110) ; x = 0x28(00101000) ; sbox = 0x72(01110010) 
not equal: i = 0x1f(00011111) ; x = 0x37(00110111) ; sbox = 0xc0(11000000) 
not equal: i = 0x20(00100000) ; x = 0x80(10000000) ; sbox = 0xb7(10110111) 
not equal: i = 0x21(00100001) ; x = 0x9f(10011111) ; sbox = 0xfd(11111101) 
not equal: i = 0x22(00100010) ; x = 0xbe(10111110) ; sbox = 0x93(10010011) 
not equal: i = 0x23(00100011) ; x = 0xa1(10100001) ; sbox = 0x26(00100110) 
not equal: i = 0x24(00100100) ; x = 0xfc(11111100) ; sbox = 0x36(00110110) 
not equal: i = 0x25(00100101) ; x = 0xe3(11100011) ; sbox = 0x3f(00111111) 
not equal: i = 0x26(00100110) ; x = 0xc2(11000010) ; sbox = 0xf7(11110111) 
not equal: i = 0x27(00100111) ; x = 0xdd(11011101) ; sbox = 0xcc(11001100) 
not equal: i = 0x28(00101000) ; x = 0x78(01111000) ; sbox = 0x34(00110100) 
not equal: i = 0x29(00101001) ; x = 0x67(01100111) ; sbox = 0xa5(10100101) 
not equal: i = 0x2a(00101010) ; x = 0x46(01000110) ; sbox = 0xe5(11100101) 
not equal: i = 0x2b(00101011) ; x = 0x59(01011001) ; sbox = 0xf1(11110001) 
not equal: i = 0x2c(00101100) ; x = 0x04(00000100) ; sbox = 0x71(01110001) 
not equal: i = 0x2d(00101101) ; x = 0x1b(00011011) ; sbox = 0xd8(11011000) 
not equal: i = 0x2e(00101110) ; x = 0x3a(00111010) ; sbox = 0x31(00110001) 
not equal: i = 0x2f(00101111) ; x = 0x25(00100101) ; sbox = 0x15(00010101) 
not equal: i = 0x30(00110000) ; x = 0x71(01110001) ; sbox = 0x04(00000100) 
not equal: i = 0x31(00110001) ; x = 0x6e(01101110) ; sbox = 0xc7(11000111) 
not equal: i = 0x32(00110010) ; x = 0x4f(01001111) ; sbox = 0x23(00100011) 
not equal: i = 0x33(00110011) ; x = 0x50(01010000) ; sbox = 0xc3(11000011) 
not equal: i = 0x34(00110100) ; x = 0x0d(00001101) ; sbox = 0x18(00011000) 
not equal: i = 0x35(00110101) ; x = 0x12(00010010) ; sbox = 0x96(10010110) 
not equal: i = 0x36(00110110) ; x = 0x33(00110011) ; sbox = 0x05(00000101) 
not equal: i = 0x37(00110111) ; x = 0x2c(00101100) ; sbox = 0x9a(10011010) 
not equal: i = 0x38(00111000) ; x = 0x89(10001001) ; sbox = 0x07(00000111) 
not equal: i = 0x39(00111001) ; x = 0x96(10010110) ; sbox = 0x12(00010010) 
not equal: i = 0x3a(00111010) ; x = 0xb7(10110111) ; sbox = 0x80(10000000) 
not equal: i = 0x3b(00111011) ; x = 0xa8(10101000) ; sbox = 0xe2(11100010) 
not equal: i = 0x3c(00111100) ; x = 0xf5(11110101) ; sbox = 0xeb(11101011) 
not equal: i = 0x3d(00111101) ; x = 0xea(11101010) ; sbox = 0x27(00100111) 
not equal: i = 0x3e(00111110) ; x = 0xcb(11001011) ; sbox = 0xb2(10110010) 
not equal: i = 0x3f(00111111) ; x = 0xd4(11010100) ; sbox = 0x75(01110101) 
not equal: i = 0x40(01000000) ; x = 0xa4(10100100) ; sbox = 0x09(00001001) 
not equal: i = 0x41(01000001) ; x = 0xbb(10111011) ; sbox = 0x83(10000011) 
not equal: i = 0x42(01000010) ; x = 0x9a(10011010) ; sbox = 0x2c(00101100) 
not equal: i = 0x43(01000011) ; x = 0x85(10000101) ; sbox = 0x1a(00011010) 
not equal: i = 0x44(01000100) ; x = 0xd8(11011000) ; sbox = 0x1b(00011011) 
not equal: i = 0x45(01000101) ; x = 0xc7(11000111) ; sbox = 0x6e(01101110) 
not equal: i = 0x46(01000110) ; x = 0xe6(11100110) ; sbox = 0x5a(01011010) 
not equal: i = 0x47(01000111) ; x = 0xf9(11111001) ; sbox = 0xa0(10100000) 
not equal: i = 0x48(01001000) ; x = 0x5c(01011100) ; sbox = 0x52(01010010) 
not equal: i = 0x49(01001001) ; x = 0x43(01000011) ; sbox = 0x3b(00111011) 
not equal: i = 0x4a(01001010) ; x = 0x62(01100010) ; sbox = 0xd6(11010110) 
not equal: i = 0x4b(01001011) ; x = 0x7d(01111101) ; sbox = 0xb3(10110011) 
not equal: i = 0x4c(01001100) ; x = 0x20(00100000) ; sbox = 0x29(00101001) 
not equal: i = 0x4d(01001101) ; x = 0x3f(00111111) ; sbox = 0xe3(11100011) 
not equal: i = 0x4e(01001110) ; x = 0x1e(00011110) ; sbox = 0x2f(00101111) 
not equal: i = 0x4f(01001111) ; x = 0x01(00000001) ; sbox = 0x84(10000100) 
not equal: i = 0x50(01010000) ; x = 0x55(01010101) ; sbox = 0x53(01010011) 
not equal: i = 0x51(01010001) ; x = 0x4a(01001010) ; sbox = 0xd1(11010001) 
not equal: i = 0x52(01010010) ; x = 0x6b(01101011) ; sbox = 0x00(00000000) 
not equal: i = 0x53(01010011) ; x = 0x74(01110100) ; sbox = 0xed(11101101) 
not equal: i = 0x54(01010100) ; x = 0x29(00101001) ; sbox = 0x20(00100000) 
not equal: i = 0x55(01010101) ; x = 0x36(00110110) ; sbox = 0xfc(11111100) 
not equal: i = 0x56(01010110) ; x = 0x17(00010111) ; sbox = 0xb1(10110001) 
not equal: i = 0x57(01010111) ; x = 0x08(00001000) ; sbox = 0x5b(01011011) 
not equal: i = 0x58(01011000) ; x = 0xad(10101101) ; sbox = 0x6a(01101010) 
not equal: i = 0x59(01011001) ; x = 0xb2(10110010) ; sbox = 0xcb(11001011) 
not equal: i = 0x5a(01011010) ; x = 0x93(10010011) ; sbox = 0xbe(10111110) 
not equal: i = 0x5b(01011011) ; x = 0x8c(10001100) ; sbox = 0x39(00111001) 
not equal: i = 0x5c(01011100) ; x = 0xd1(11010001) ; sbox = 0x4a(01001010) 
not equal: i = 0x5d(01011101) ; x = 0xce(11001110) ; sbox = 0x4c(01001100) 
not equal: i = 0x5e(01011110) ; x = 0xef(11101111) ; sbox = 0x58(01011000) 
not equal: i = 0x5f(01011111) ; x = 0xf0(11110000) ; sbox = 0xcf(11001111) 
not equal: i = 0x60(01100000) ; x = 0x47(01000111) ; sbox = 0xd0(11010000) 
not equal: i = 0x61(01100001) ; x = 0x58(01011000) ; sbox = 0xef(11101111) 
not equal: i = 0x62(01100010) ; x = 0x79(01111001) ; sbox = 0xaa(10101010) 
not equal: i = 0x63(01100011) ; x = 0x66(01100110) ; sbox = 0xfb(11111011) 
not equal: i = 0x64(01100100) ; x = 0x3b(00111011) ; sbox = 0x43(01000011) 
not equal: i = 0x65(01100101) ; x = 0x24(00100100) ; sbox = 0x4d(01001101) 
not equal: i = 0x66(01100110) ; x = 0x05(00000101) ; sbox = 0x33(00110011) 
not equal: i = 0x67(01100111) ; x = 0x1a(00011010) ; sbox = 0x85(10000101) 
not equal: i = 0x68(01101000) ; x = 0xbf(10111111) ; sbox = 0x45(01000101) 
not equal: i = 0x69(01101001) ; x = 0xa0(10100000) ; sbox = 0xf9(11111001) 
not equal: i = 0x6a(01101010) ; x = 0x81(10000001) ; sbox = 0x02(00000010) 
not equal: i = 0x6b(01101011) ; x = 0x9e(10011110) ; sbox = 0x7f(01111111) 
not equal: i = 0x6c(01101100) ; x = 0xc3(11000011) ; sbox = 0x50(01010000) 
not equal: i = 0x6d(01101101) ; x = 0xdc(11011100) ; sbox = 0x3c(00111100) 
not equal: i = 0x6e(01101110) ; x = 0xfd(11111101) ; sbox = 0x9f(10011111) 
not equal: i = 0x6f(01101111) ; x = 0xe2(11100010) ; sbox = 0xa8(10101000) 
not equal: i = 0x70(01110000) ; x = 0xb6(10110110) ; sbox = 0x51(01010001) 
not equal: i = 0x71(01110001) ; x = 0xa9(10101001) ; sbox = 0xa3(10100011) 
not equal: i = 0x72(01110010) ; x = 0x88(10001000) ; sbox = 0x40(01000000) 
not equal: i = 0x73(01110011) ; x = 0x97(10010111) ; sbox = 0x8f(10001111) 
not equal: i = 0x74(01110100) ; x = 0xca(11001010) ; sbox = 0x92(10010010) 
not equal: i = 0x75(01110101) ; x = 0xd5(11010101) ; sbox = 0x9d(10011101) 
not equal: i = 0x76(01110110) ; x = 0xf4(11110100) ; sbox = 0x38(00111000) 
not equal: i = 0x77(01110111) ; x = 0xeb(11101011) ; sbox = 0xf5(11110101) 
not equal: i = 0x78(01111000) ; x = 0x4e(01001110) ; sbox = 0xbc(10111100) 
not equal: i = 0x79(01111001) ; x = 0x51(01010001) ; sbox = 0xb6(10110110) 
not equal: i = 0x7a(01111010) ; x = 0x70(01110000) ; sbox = 0xda(11011010) 
not equal: i = 0x7b(01111011) ; x = 0x6f(01101111) ; sbox = 0x21(00100001) 
not equal: i = 0x7c(01111100) ; x = 0x32(00110010) ; sbox = 0x10(00010000) 
not equal: i = 0x7d(01111101) ; x = 0x2d(00101101) ; sbox = 0xff(11111111) 
not equal: i = 0x7e(01111110) ; x = 0x0c(00001100) ; sbox = 0xf3(11110011) 
not equal: i = 0x7f(01111111) ; x = 0x13(00010011) ; sbox = 0xd2(11010010) 
not equal: i = 0x80(10000000) ; x = 0xec(11101100) ; sbox = 0xcd(11001101) 
not equal: i = 0x81(10000001) ; x = 0xf3(11110011) ; sbox = 0x0c(00001100) 
not equal: i = 0x82(10000010) ; x = 0xd2(11010010) ; sbox = 0x13(00010011) 
not equal: i = 0x83(10000011) ; x = 0xcd(11001101) ; sbox = 0xec(11101100) 
not equal: i = 0x84(10000100) ; x = 0x90(10010000) ; sbox = 0x5f(01011111) 
not equal: i = 0x85(10000101) ; x = 0x8f(10001111) ; sbox = 0x97(10010111) 
not equal: i = 0x86(10000110) ; x = 0xae(10101110) ; sbox = 0x44(01000100) 
not equal: i = 0x87(10000111) ; x = 0xb1(10110001) ; sbox = 0x17(00010111) 
not equal: i = 0x88(10001000) ; x = 0x14(00010100) ; sbox = 0xc4(11000100) 
not equal: i = 0x89(10001001) ; x = 0x0b(00001011) ; sbox = 0xa7(10100111) 
not equal: i = 0x8a(10001010) ; x = 0x2a(00101010) ; sbox = 0x7e(01111110) 
not equal: i = 0x8b(10001011) ; x = 0x35(00110101) ; sbox = 0x3d(00111101) 
not equal: i = 0x8c(10001100) ; x = 0x68(01101000) ; sbox = 0x64(01100100) 
not equal: i = 0x8d(10001101) ; x = 0x77(01110111) ; sbox = 0x5d(01011101) 
not equal: i = 0x8e(10001110) ; x = 0x56(01010110) ; sbox = 0x19(00011001) 
not equal: i = 0x8f(10001111) ; x = 0x49(01001001) ; sbox = 0x73(01110011) 
not equal: i = 0x90(10010000) ; x = 0x1d(00011101) ; sbox = 0x60(01100000) 
not equal: i = 0x91(10010001) ; x = 0x02(00000010) ; sbox = 0x81(10000001) 
not equal: i = 0x92(10010010) ; x = 0x23(00100011) ; sbox = 0x4f(01001111) 
not equal: i = 0x93(10010011) ; x = 0x3c(00111100) ; sbox = 0xdc(11011100) 
not equal: i = 0x94(10010100) ; x = 0x61(01100001) ; sbox = 0x22(00100010) 
not equal: i = 0x95(10010101) ; x = 0x7e(01111110) ; sbox = 0x2a(00101010) 
not equal: i = 0x96(10010110) ; x = 0x5f(01011111) ; sbox = 0x90(10010000) 
not equal: i = 0x97(10010111) ; x = 0x40(01000000) ; sbox = 0x88(10001000) 
not equal: i = 0x98(10011000) ; x = 0xe5(11100101) ; sbox = 0x46(01000110) 
not equal: i = 0x99(10011001) ; x = 0xfa(11111010) ; sbox = 0xee(11101110) 
not equal: i = 0x9a(10011010) ; x = 0xdb(11011011) ; sbox = 0xb8(10111000) 
not equal: i = 0x9b(10011011) ; x = 0xc4(11000100) ; sbox = 0x14(00010100) 
not equal: i = 0x9c(10011100) ; x = 0x99(10011001) ; sbox = 0xde(11011110) 
not equal: i = 0x9d(10011101) ; x = 0x86(10000110) ; sbox = 0x5e(01011110) 
not equal: i = 0x9e(10011110) ; x = 0xa7(10100111) ; sbox = 0x0b(00001011) 
not equal: i = 0x9f(10011111) ; x = 0xb8(10111000) ; sbox = 0xdb(11011011) 
not equal: i = 0xa0(10100000) ; x = 0x0f(00001111) ; sbox = 0xe0(11100000) 
not equal: i = 0xa1(10100001) ; x = 0x10(00010000) ; sbox = 0x32(00110010) 
not equal: i = 0xa2(10100010) ; x = 0x31(00110001) ; sbox = 0x3a(00111010) 
not equal: i = 0xa3(10100011) ; x = 0x2e(00101110) ; sbox = 0x0a(00001010) 
not equal: i = 0xa4(10100100) ; x = 0x73(01110011) ; sbox = 0x49(01001001) 
not equal: i = 0xa5(10100101) ; x = 0x6c(01101100) ; sbox = 0x06(00000110) 
not equal: i = 0xa6(10100110) ; x = 0x4d(01001101) ; sbox = 0x24(00100100) 
not equal: i = 0xa7(10100111) ; x = 0x52(01010010) ; sbox = 0x5c(01011100) 
not equal: i = 0xa8(10101000) ; x = 0xf7(11110111) ; sbox = 0xc2(11000010) 
not equal: i = 0xa9(10101001) ; x = 0xe8(11101000) ; sbox = 0xd3(11010011) 
not equal: i = 0xaa(10101010) ; x = 0xc9(11001001) ; sbox = 0xac(10101100) 
not equal: i = 0xab(10101011) ; x = 0xd6(11010110) ; sbox = 0x62(01100010) 
not equal: i = 0xac(10101100) ; x = 0x8b(10001011) ; sbox = 0x91(10010001) 
not equal: i = 0xad(10101101) ; x = 0x94(10010100) ; sbox = 0x95(10010101) 
not equal: i = 0xae(10101110) ; x = 0xb5(10110101) ; sbox = 0xe4(11100100) 
not equal: i = 0xaf(10101111) ; x = 0xaa(10101010) ; sbox = 0x79(01111001) 
not equal: i = 0xb0(10110000) ; x = 0xfe(11111110) ; sbox = 0xe7(11100111) 
not equal: i = 0xb1(10110001) ; x = 0xe1(11100001) ; sbox = 0xc8(11001000) 
not equal: i = 0xb2(10110010) ; x = 0xc0(11000000) ; sbox = 0x37(00110111) 
not equal: i = 0xb3(10110011) ; x = 0xdf(11011111) ; sbox = 0x6d(01101101) 
not equal: i = 0xb4(10110100) ; x = 0x82(10000010) ; sbox = 0x8d(10001101) 
not equal: i = 0xb5(10110101) ; x = 0x9d(10011101) ; sbox = 0xd5(11010101) 
not equal: i = 0xb6(10110110) ; x = 0xbc(10111100) ; sbox = 0x4e(01001110) 
not equal: i = 0xb7(10110111) ; x = 0xa3(10100011) ; sbox = 0xa9(10101001) 
not equal: i = 0xb8(10111000) ; x = 0x06(00000110) ; sbox = 0x6c(01101100) 
not equal: i = 0xb9(10111001) ; x = 0x19(00011001) ; sbox = 0x56(01010110) 
not equal: i = 0xba(10111010) ; x = 0x38(00111000) ; sbox = 0xf4(11110100) 
not equal: i = 0xbb(10111011) ; x = 0x27(00100111) ; sbox = 0xea(11101010) 
not equal: i = 0xbc(10111100) ; x = 0x7a(01111010) ; sbox = 0x65(01100101) 
not equal: i = 0xbd(10111101) ; x = 0x65(01100101) ; sbox = 0x7a(01111010) 
not equal: i = 0xbe(10111110) ; x = 0x44(01000100) ; sbox = 0xae(10101110) 
not equal: i = 0xbf(10111111) ; x = 0x5b(01011011) ; sbox = 0x08(00001000) 
not equal: i = 0xc0(11000000) ; x = 0x2b(00101011) ; sbox = 0xba(10111010) 
not equal: i = 0xc1(11000001) ; x = 0x34(00110100) ; sbox = 0x78(01111000) 
not equal: i = 0xc2(11000010) ; x = 0x15(00010101) ; sbox = 0x25(00100101) 
not equal: i = 0xc3(11000011) ; x = 0x0a(00001010) ; sbox = 0x2e(00101110) 
not equal: i = 0xc4(11000100) ; x = 0x57(01010111) ; sbox = 0x1c(00011100) 
not equal: i = 0xc5(11000101) ; x = 0x48(01001000) ; sbox = 0xa6(10100110) 
not equal: i = 0xc6(11000110) ; x = 0x69(01101001) ; sbox = 0xb4(10110100) 
not equal: i = 0xc7(11000111) ; x = 0x76(01110110) ; sbox = 0xc6(11000110) 
not equal: i = 0xc8(11001000) ; x = 0xd3(11010011) ; sbox = 0xe8(11101000) 
not equal: i = 0xc9(11001001) ; x = 0xcc(11001100) ; sbox = 0xdd(11011101) 
not equal: i = 0xca(11001010) ; x = 0xed(11101101) ; sbox = 0x74(01110100) 
not equal: i = 0xcb(11001011) ; x = 0xf2(11110010) ; sbox = 0x1f(00011111) 
not equal: i = 0xcc(11001100) ; x = 0xaf(10101111) ; sbox = 0x4b(01001011) 
not equal: i = 0xcd(11001101) ; x = 0xb0(10110000) ; sbox = 0xbd(10111101) 
not equal: i = 0xce(11001110) ; x = 0x91(10010001) ; sbox = 0x8b(10001011) 
not equal: i = 0xcf(11001111) ; x = 0x8e(10001110) ; sbox = 0x8a(10001010) 
not equal: i = 0xd0(11010000) ; x = 0xda(11011010) ; sbox = 0x70(01110000) 
not equal: i = 0xd1(11010001) ; x = 0xc5(11000101) ; sbox = 0x3e(00111110) 
not equal: i = 0xd2(11010010) ; x = 0xe4(11100100) ; sbox = 0xb5(10110101) 
not equal: i = 0xd3(11010011) ; x = 0xfb(11111011) ; sbox = 0x66(01100110) 
not equal: i = 0xd4(11010100) ; x = 0xa6(10100110) ; sbox = 0x48(01001000) 
not equal: i = 0xd5(11010101) ; x = 0xb9(10111001) ; sbox = 0x03(00000011) 
not equal: i = 0xd6(11010110) ; x = 0x98(10011000) ; sbox = 0xf6(11110110) 
not equal: i = 0xd7(11010111) ; x = 0x87(10000111) ; sbox = 0x0e(00001110) 
not equal: i = 0xd8(11011000) ; x = 0x22(00100010) ; sbox = 0x61(01100001) 
not equal: i = 0xd9(11011001) ; x = 0x3d(00111101) ; sbox = 0x35(00110101) 
not equal: i = 0xda(11011010) ; x = 0x1c(00011100) ; sbox = 0x57(01010111) 
not equal: i = 0xdb(11011011) ; x = 0x03(00000011) ; sbox = 0xb9(10111001) 
not equal: i = 0xdc(11011100) ; x = 0x5e(01011110) ; sbox = 0x86(10000110) 
not equal: i = 0xdd(11011101) ; x = 0x41(01000001) ; sbox = 0xc1(11000001) 
not equal: i = 0xde(11011110) ; x = 0x60(01100000) ; sbox = 0x1d(00011101) 
not equal: i = 0xdf(11011111) ; x = 0x7f(01111111) ; sbox = 0x9e(10011110) 
not equal: i = 0xe0(11100000) ; x = 0xc8(11001000) ; sbox = 0xe1(11100001) 
not equal: i = 0xe1(11100001) ; x = 0xd7(11010111) ; sbox = 0xf8(11111000) 
not equal: i = 0xe2(11100010) ; x = 0xf6(11110110) ; sbox = 0x98(10011000) 
not equal: i = 0xe3(11100011) ; x = 0xe9(11101001) ; sbox = 0x11(00010001) 
not equal: i = 0xe4(11100100) ; x = 0xb4(10110100) ; sbox = 0x69(01101001) 
not equal: i = 0xe5(11100101) ; x = 0xab(10101011) ; sbox = 0xd9(11011001) 
not equal: i = 0xe6(11100110) ; x = 0x8a(10001010) ; sbox = 0x8e(10001110) 
not equal: i = 0xe7(11100111) ; x = 0x95(10010101) ; sbox = 0x94(10010100) 
not equal: i = 0xe8(11101000) ; x = 0x30(00110000) ; sbox = 0x9b(10011011) 
not equal: i = 0xe9(11101001) ; x = 0x2f(00101111) ; sbox = 0x1e(00011110) 
not equal: i = 0xea(11101010) ; x = 0x0e(00001110) ; sbox = 0x87(10000111) 
not equal: i = 0xeb(11101011) ; x = 0x11(00010001) ; sbox = 0xe9(11101001) 
not equal: i = 0xec(11101100) ; x = 0x4c(01001100) ; sbox = 0xce(11001110) 
not equal: i = 0xed(11101101) ; x = 0x53(01010011) ; sbox = 0x55(01010101) 
not equal: i = 0xee(11101110) ; x = 0x72(01110010) ; sbox = 0x28(00101000) 
not equal: i = 0xef(11101111) ; x = 0x6d(01101101) ; sbox = 0xdf(11011111) 
not equal: i = 0xf0(11110000) ; x = 0x39(00111001) ; sbox = 0x8c(10001100) 
not equal: i = 0xf1(11110001) ; x = 0x26(00100110) ; sbox = 0xa1(10100001) 
not equal: i = 0xf2(11110010) ; x = 0x07(00000111) ; sbox = 0x89(10001001) 
not equal: i = 0xf3(11110011) ; x = 0x18(00011000) ; sbox = 0x0d(00001101) 
not equal: i = 0xf4(11110100) ; x = 0x45(01000101) ; sbox = 0xbf(10111111) 
not equal: i = 0xf5(11110101) ; x = 0x5a(01011010) ; sbox = 0xe6(11100110) 
not equal: i = 0xf6(11110110) ; x = 0x7b(01111011) ; sbox = 0x42(01000010) 
not equal: i = 0xf7(11110111) ; x = 0x64(01100100) ; sbox = 0x68(01101000) 
not equal: i = 0xf8(11111000) ; x = 0xc1(11000001) ; sbox = 0x41(01000001) 
not equal: i = 0xf9(11111001) ; x = 0xde(11011110) ; sbox = 0x99(10011001) 
not equal: i = 0xfa(11111010) ; x = 0xff(11111111) ; sbox = 0x2d(00101101) 
not equal: i = 0xfb(11111011) ; x = 0xe0(11100000) ; sbox = 0x0f(00001111) 
not equal: i = 0xfc(11111100) ; x = 0xbd(10111101) ; sbox = 0xb0(10110000) 
not equal: i = 0xfd(11111101) ; x = 0xa2(10100010) ; sbox = 0x54(01010100) 
not equal: i = 0xfe(11111110) ; x = 0x83(10000011) ; sbox = 0xbb(10111011) 
not equal: i = 0xff(11111111) ; x = 0x9c(10011100) ; sbox = 0xbb(10111011)

Kann mir vielleicht jemand einen Hinweis geben was da jetzt der Fehler 
ist?
Ich verzweifle dran.

Vielen Herzlichen Dank
Gruß Leo

[(prx) A. K. (prx)]

Das "multiplicative inverse" von i ist i?

[Leo B. (luigi)]

A. K. schrieb:
> Das "multiplicative inverse" von i ist i?

Nein, ich dachte man muss x und s mit dem "multiplicative inverse" des 
Ergebnisses setzten. Wie würde man das sonst errechnen?

[(prx) A. K. (prx)]

Leo B. schrieb:
> Nein, ich dachte man muss x und s mit dem "multiplicative inverse" des
> Ergebnisses setzten.

Bei "Store the multiplicative inverse of the input number in two 8-bit 
unsigned temporary variables: s and x."? Interessante Interpretation.

> Wie würde man das sonst errechnen?

Du könntest nachschlagen, was das bedeutet. Bei gewöhnlicher Arithmetik 
wärs der Kehrwert, das schon mal als kleine Hilfe (à la Jauch ;-).

[Detlef K. (adenin)]

Das ist aber keine gewöhnliche Arithmetik.
Das ist ungewöhnlich grausame Arithmetik. :)
Schau mal http://www.cs.utsa.edu/~wagner/laws/FFM.html ganz unten.

[Johannes O. (jojo_2)]

Die Berechnung erfolg auf einem Finiten Feld. Genauer gesagt: GF(256) 
oder auch GF(2^8) genannt. Außerdem wird auch auf GF(2) gerechnet.

Damit du eine Chance hast zu verstehen was da passiert, musst du zuerst 
verstehen, wie man auf diesen Feldern rechnet und was diese 
Bezeichnungen hier bedeuten.

Entweder du findest selbst etwas dazu oder du schaust es dir hier an, um 
nen groben Überblick zu bekommen: (FIPS-197), Kapitel 4
http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf


Die Berechnung der SBox selbst besteht aus zwei Teilen: Einer affinen 
Transformation auf GF(2) (stark vereinfach gesagt: einen Wert mit einer 
Konstante multiplizieren und dann eine Konstante addieren. Das ganze 
passiert Bitweise), und dem Berechnen des multiplikativen Inversen (das 
passiert auf GF(256)).

Das Inverse wird wie schon geschrieben auf GF(256) berechnet. D.h., dass 
AUF DEM FINITEN FELD gelten muss, dass deine Zahl multipliziert mit 
seinem Inversen, 1 ergeben muss.

Fürs Berechnen des Inversen gibts mehrere Möglichkeiten. Wie diese 
funktionieren ist relativ schwierig zu erklären und das kann man erst 
verstehen, sofern man die Grundlagen der Mathematik dahinter sehr gut 
verstanden hat.
Eine Möglichkeit ist, dass man das Problem mithilfe von Logarithmen 
löst. Da verwendet man einen Generator des GF(256), z.B. 0x03 wäre 
einer, und macht eine Art Brute-Force suche des Inversen, wobei man 
immer nur mit 0x03 multiplizieren muss, was recht schnell geht. Das 
führt an dieser Stelle aber zu weit, das würde erstmal verwirren.


Detlef Kunz schrieb:
> che Arithmetik.
> Das ist ungewöhnlich grausame Arithmetik. :)
> Schau mal http://www.cs.utsa.edu/~wagner/laws/FFM.html ganz unten.

Hier ist diese Methode ja auch genauer beschrieben, sollte auch 
verständlich sein.
Als grausam würd ich das nicht bezeichnen, ich finde sowas ehrlich 
gesagt sogar ziemlich schön! :-) Früher kams bei mal in Höherer 
Mathematik dran, aber das haben sie dann leider wieder gestrichen...